The significance of the Dirac notation

[PeterDonis]

in the first option, both up arrows signify state $e_A$. In the second option both up arrows signify state $e_B$.

Then you should make this clear by using the subscripts and writing these two distinct states as $| \uparrow_A \uparrow_A \rangle$ and $| \uparrow_B \uparrow_B \rangle$. Otherwise you'll just confuse people, including yourself.

 

[entropy1]

Then you should make this clear by using the subscripts and writing these two distinct states as $| \uparrow_A \uparrow_A \rangle$ and $| \uparrow_B \uparrow_B \rangle$. Otherwise you'll just confuse people, including yourself.

Yes, I was thinking along this line myself. I thought perhaps $| \uparrow_A \uparrow_A \rangle + | \uparrow_B \uparrow_B \rangle$ might do the trick. Or perhaps it should be $| \uparrow_A \uparrow_A \rangle + | \uparrow_B \uparrow_B \rangle + | \downarrow_A \downarrow_A \rangle + | \downarrow_B \downarrow_B \rangle$.

 

[PeterDonis]

I thought perhaps $| \uparrow_A \uparrow_A \rangle + | \uparrow_B \uparrow_B \rangle$ might do the trick.

That is a different state of the two-qubit system than any of the ones we have been talking about up to now. Which state do you want to talk about?

 

[entropy1]

That is a different state of the two-qubit system than any of the ones we have been talking about up to now. Which state do you want to talk about?

Sorry, I mean an entangled state thereby.

It was just a hunch.

 

[PeterDonis]

I mean an entangled state thereby.

An entangled state would be something like $1 / \sqrt{2} \left( | \uparrow_A \uparrow_A \rangle + | \downarrow_A \downarrow_A \rangle \right)$.

 

[entropy1]

A different way to put my question is: Suppose we can write our entangled state as $|\uparrow\downarrow\rangle + |\downarrow\uparrow\rangle$ and observe that the first entries in both sub-states represents the possible outcome that we supposedly to measure. The physical manifestation of the outcome however may differ according to the orientation of the measurement basis. So the arrow of this first entry is not representing a known physical manifestation until we have measured an outcome and associate that outcome with one of the two possible arrows in the first entry. Then, after the measurement of the first entry yields either spin up or down, people seem to assert that the spin of the other particle (the second entry) is in fact either up or down too with respect to the orientation of the spin of the first particle. Thus, we claim to only know the spin of the first particle after having measured it, but know the spin of the other particle while not having measured it. And if the measurement basis of the second particle has a different orientation from the basis of the first particle, the arrow of this second particle cannot represent the actual outcome, while the first arrow is supposed to do just that! what is left of the meaning of up arrow or down arrow in the entangled state? Does the entangled state mean to represent measurement outcomes? It doesn't seem so at all! The the up arrow and the down arrow seem to represent nothing at all!

You can see it thus also: suppose the SGM's have a 45 degree angle from each other: SGM A 0 degrees and SGM B 45 degrees. If we assume the first entry is measured first, up arrow means 0 degrees and down arrow means 180 degrees. If we assume the second entry is measured first, up arrow means 45 degrees and down arrow means 225 degrees. So the meaning of the arrows vary depending on who is supposedly measuring first.

 

[PeroK]

Either you understand what a state represents or you don't. If you do, the meaning is clear. Your attempt to describe a state in these terms indicates that you have not grasped the mathematical formalism and relationship between a state and all possible measurement outcomes.

 

[entropy1]

Either you understand what a state represents or you don't. If you do, the meaning is clear. Your attempt to describe a state in these terms indicates that you have not grasped the mathematical formalism and relationship between a state and all possible measurement outcomes.

Could well be. You probably conclude that from the "muddyness" of my argument. Or just the math of QM prevails. I hope this is clearer?:

You can see it thus also: suppose the SGM's have a 45 degree angle from each other: SGM A 0 degrees and SGM B 45 degrees. If we assume the first entry is measured first, up arrow means 0 degrees and down arrow means 180 degrees. If we assume the second entry is measured first, up arrow means 45 degrees and down arrow means 225 degrees. So the meaning of the arrows vary depending on who is supposedly measuring first.

From this it should be clear what I mean.

I guess that Dirac notation is equivalent to other notations, so Dirac is probably not the problem here.

Me against the physics community lol

 

[PeroK]

Could well be. You probably conclude that from the "muddyness" of my argument. Or just the math of QM prevails. I hope this is clearer?:

It's not an argument, as such. It's just a muddy way of trying to say what can be said more simply.

So the meaning of the arrows vary depending on who is supposedly measuring first.

In any case, you've ended up at this patently false conclusion.

 

[PeroK]

Or just the math of QM prevails.

You could check out this thread for how to understand these states in terms of different measurement axes:

https://www.physicsforums.com/threa...s-in-two-different-basis.993252/#post-6388834

 

[PeterDonis]

Me against the physics community lol

And you will lose.

Enough is enough. Thread closed.